The effect of block parameter perturbations in Gaussian Bayesian networks: Sensitivity and robustness

Gómez–Villegas, Miguel A.; Maı́n, Paloma; García, Rosario Susi

doi:10.1016/j.ins.2012.08.004

Cited by 16 publications

(14 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, given this algebraic characterization, we demonstrate that one-way sensitivity methods defined for BNs can be generalized to single full CPT analyses for any model whose interpolating polynomial is multilinear, for example context-specific BNs [3] and stratified chain event graphs [12,39]. Because of both the lack of theoretical results justifying their use and the increase in computational complexity, multi-way methods have not been extensively discussed in the literature: see [2,7,21] for some exceptions. This paper aims at providing a comprehensive theoretical toolbox to start applying such analyses in practice.…”

Section: Introductionmentioning

confidence: 99%

“…[31] for a review), including the famous Kullback-Leibler (KL) divergence [28]. The application of KL distances in sensitivity analyses of BNs has been almost exclusively restricted to the case when the underlying distribution is assumed Gaussian [20,21], because in discrete BNs the computation of such a divergence requires more computational power than for CD distances. We demonstrate below that this additional complexity is a feature shared by any divergence in the family of φ-divergences.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sensitivity analysis in multilinear probabilistic models

Leonelli

Görgen

Smith

2017

Information Sciences

View full text Add to dashboard Cite

Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the impact of a parameter change to the Chan-Darwiche distance. Although not fully recognized, the majority of these results rely heavily on the multilinear structure of atomic probabilities in terms of the conditional probability parameters associated with this type of network. By defining a statistical model through the polynomial expression of its associated defining conditional probabilities, we develop here a unifying approach to sensitivity methods applicable to a large suite of models including extensions of Bayesian networks, for instance context-specific ones. Our algebraic approach enables us to prove that for models whose defining polynomial is multilinear both the Chan-Darwiche distance and any divergence in the family of φ-divergences are minimized for a certain class of multi-parameter contemporaneous variations when parameters are proportionally covaried.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis in multilinear probabilistic models

Leonelli

Görgen

Smith

2017

Information Sciences

View full text Add to dashboard Cite

show abstract

“…The CD distance is used to quantify global changes by measuring how the overall distribution behaves when one (or more) parameter is varied. Likewise, SA approaches have been developed for continuous BBNs (mostly based on linear Gaussian regression) either based on computing partial derivatives (Castillo & Kjaerulff 2003) or based on the use of divergence measures (Gómez-Villegas et al, 2007), with generalisation to multi-way SA (Gómez-Villegas et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis of Bayesian networks to parameters of the conditional probability model using a Beta regression approach

Rohmer

Gehl

2020

Expert Systems with Applications

View full text Add to dashboard Cite

Ensuring the validity and credibility of Bayesian Belief Network (BBN) as a modelling tool for expert systems requires appropriate methods for sensitivity analysis (SA), in order to test the robustness of the BBN diagnostic and prognostic with respect to the parameterisation of the conditional probability model (CPM). Yet, the most widely used techniques (based on sensitivity functions for discrete BBNs) only provide a local insight on the CPM influence, i.e. by varying only one CPM parameter at a time (or a few of them) while keeping the other ones unchanged. To overcome this limitation, the present study proposes an approach for global SA relying on Beta Regression using gradient boosting (potentially combined with stability selection analysis): it presents the benefit of keeping the presentation intuitive through a graphbased approach, while being applicable to a large number of CPM parameters. The implementation of this approach is investigated for three cases, which cover a large spectrum of situations: (1) a small discrete BBN, used to capture medical knowledge, demonstrates the proposed approach; (2) a linear Gaussian BBN, used to assess the damage of reinforced concrete structures, exemplifies a case where the number of parameters is too large to be easily processed and interpreted (>40 parameters); (3) a discrete BBN, used for reliability analysis of nuclear power plant, exemplifies a case where analytical solutions for sensitivity can hardly be 2 derived. Finally, provided that the validity of the BBR model is carefully checked, we show that the proposed approach can provide richer information than traditional SA methods at different levels: (i) it selects the most influential parameters; (ii) it provides the functional relation between the CPM parameter and the result of the probabilistic query; and (iii) it identifies how the CPM parameters can lead to situations of high probability, while quantifying the confidence in the occurrence of these situations.

show abstract

“…Although mathematically convenient for many problems, in complex systems modeling, independence assumption is not reasonable because much of the information is somehow encoded in the relations between the random variables [20,21]. In order to overcome this limitation, Markov Random Field (MRF) models appear as a natural generalization of the classical approach by the replacement of the independence assumption by a more realistic conditional independence assumption.…”

Section: Introductionmentioning

confidence: 99%

Learning from Complex Systems: On the Roles of Entropy and Fisher Information in Pairwise Isotropic Gaussian Markov Random Fields

Levada

2014

Entropy

View full text Add to dashboard Cite

Markov random field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In this paper, our goal is to enlighten the connection between Fisher information, Shannon entropy, information geometry and the behavior of complex systems modeled by isotropic pairwise Gaussian Markov random fields. We propose analytical expressions to compute local and global versions of these measures using Besag's pseudo-likelihood function, characterizing the system's behavior through its Fisher curve , a parametric trajectory across the information space that provides a geometric representation for the study of complex systems in which temperature deviates from infinity. Computational experiments show how the proposed tools can be useful in extracting relevant information from complex patterns. The obtained results quantify and support our main conclusion, which is: in terms of information, moving towards higher entropy states (A -> B) is different from moving towards lower entropy states (B -> A), since the Fisher curves are not the same, given a natural orientation (the direction of time).

show abstract

The effect of block parameter perturbations in Gaussian Bayesian networks: Sensitivity and robustness

Cited by 16 publications

References 21 publications

Sensitivity analysis in multilinear probabilistic models

Sensitivity analysis in multilinear probabilistic models

Sensitivity analysis of Bayesian networks to parameters of the conditional probability model using a Beta regression approach

Learning from Complex Systems: On the Roles of Entropy and Fisher Information in Pairwise Isotropic Gaussian Markov Random Fields

Contact Info

Product

Resources

About